Solve for $x$ : $x^2 - 11x + 30 = 0$
Solution: The coefficient on the $x$ term is $-11$ and the constant term is $30$ , so we need to find two numbers that add up to $-11$ and multiply to $30$ The two numbers $-6$ and $-5$ satisfy both conditions: $ {-6} + {-5} = {-11} $ $ {-6} \times {-5} = {30} $ $(x {-6}) (x {-5}) = 0$ Since the following equation is true we know that one or both quantities must equal zero. $(x -6) (x -5) = 0$ $x - 6 = 0$ or $x - 5 = 0$ Thus, $x = 6$ and $x = 5$ are the solutions.